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Radioactivity generates heat within the mantle, while mantle convection removes heat.  Because the radioactivity slowly decays, the temperature within the mantle declines and mantle convection becomes less vigorous.  Thus geological activity should also slow down.  However during the first 1-2 billion years of Earth history the mantle may have been episodically stratified, convecting in two separate layers.  Occasional breakdown of the layering would have caused dramatic episodes of volcanism and other tectonic activity. Mantle convection also governs the chemical evolution of the mantle, because volcanism at mid-ocean ridges and island arcs removes materials, whereas subduction injects a heterogeneous package back into the mantle to be stirred around.  Numerical models are used to model these processes and interpret the geochemical observations.

Relevant papers:

• Davies, G. F. (2002), Stirring geochemistry in mantle convection models with stiff plates and slabs, Geochim. Cosmochim. Acta , 66 , 3125-3142.
• Davies, G. F. (2006), Gravitational depletion of the early Earth's upper mantle and the viability of early plate tectonics, Earth Planet. Sci. Lett. , 243 , 376-382.
• Davies, G. F. (2007), Episodic layering of the early mantle by the 'basalt barrier' mechanism: implications for tectonic and geochemical evolution, Geochem. Geophys. Geosystems, submitted.